Automated Discovery of Improved Constant Weight Binary Codes

A constant weight binary code consists of n-bit binary codewords, each with exactly w bits equal to 1, such that any two codewords are at least Hamming distance d apart. A(n,d,w) is the maximum size of a constant weight binary code with parameters n,d,w. We establish improved lower bounds on A(n,d,w) by constructing new larger codes, for 24 values of (n,d,w) with 6 ≤ d ≤ 18 and 18 ≤ n ≤ 35. The improved lower bounds come from two strategies. The first is a tabu search that operates at the level of bit swaps. The second is a novel greedy heuristic that repeatedly chooses the candidate codeword that maximizes a randomly-scored histogram of distances to previously-added codewords. These strategies were proposed by CPro1, an automated protocol that generates, implements, and tests diverse strategies for combinatorial constructions.